Ambassador works well.
What is your conception of the Galactic Republic? Because I never saw a problem with Senators being from different planets as I saw it as Senators from different American states all going to Washington, DC (and then each state has its governor, and typically its own senate and lower house). So is your current galactic government much looser, more than the UN? And maybe later Palpatine establishes a true galactic government with senators coming from the planets (since it's important that he later abolishes the senate)?
Quite right to not put everything in the crawl. And I also like the three-planet pattern, unless of course the story truly calls for more.